Models developed by recent economic literature do not manage to account simultaneously for the three main stylized facts observed in many EU countries since the mid-seventies: (i) the increase in the overall unemployment rate; (ii) the difference between high-skilled and low-skilled unemployment; (iii) the stability of relative wages. This paper focuses on these issues. We construct an intertemporal general equilibrium model seeking to reproduce these facts. We consider two types of jobs and two types of workers. We allow for job competition between high- and low-skilled workers on the low-skilled segment of the labor market and for on-the-job search. Matching processes are represented by matching functions à la Pissarides. Low-skilled search intensities are endogenous and high-skilled workers decide on the amount of effort they devote to search in each labor market segment. Biased technological change is introduced via embodied technical progress and capital-skill complementarity. The model is calibrated and simulated to evaluate the impact of various types of shocks. The model reproduces quite well the unemployment rate changes and the relative wage stability observed over the past two decades